Q111 / 150 · MHT CET 2024 (10 May Shift 2) · Physics
A particle of mass ' $m$ ' performs uniform circular motion of radius ' $r$ ' with linear speed ' $v$ ' under the application of force ' $F$ '. If ' $m$ ', ' $v$ ' and ' $r$ ' are all increased by $20 \%$ the necessary change in force required to maintain the particle in uniform circular motion, is
- A$12 \%$
- B$14 \%$
- Correct answerC$44 \%$
- D$144 \%$
Solution
Let initial force be,
$F_1=\frac{m^2}{r}$
After $20 \%$ increase in all $\mathrm{m}, \mathrm{v}$ and r , $\begin{array}{ll} & \mathrm{F}_2=\frac{1.2 \mathrm{~m} \times(1.2 \mathrm{v})^2}{1.2 \mathrm{r}}=1.44 \frac{\mathrm{mv}^2}{\mathrm{r}}=1.44 \mathrm{~F}_1 \\ \therefore \quad & \mathrm{~F}_2-\mathrm{F}_1=0.44 \mathrm{~F}_1 \\ \therefore \quad & \frac{\mathrm{~F}_2-\mathrm{F}_1}{\mathrm{~F}_1} \times 100=44 \% \end{array}$ i.e., increase in force required is $44 \%$
After $20 \%$ increase in all $\mathrm{m}, \mathrm{v}$ and r , $\begin{array}{ll} & \mathrm{F}_2=\frac{1.2 \mathrm{~m} \times(1.2 \mathrm{v})^2}{1.2 \mathrm{r}}=1.44 \frac{\mathrm{mv}^2}{\mathrm{r}}=1.44 \mathrm{~F}_1 \\ \therefore \quad & \mathrm{~F}_2-\mathrm{F}_1=0.44 \mathrm{~F}_1 \\ \therefore \quad & \frac{\mathrm{~F}_2-\mathrm{F}_1}{\mathrm{~F}_1} \times 100=44 \% \end{array}$ i.e., increase in force required is $44 \%$
Hence, the correct answer is option: 'C'.